Is it permissible for a female student to take recordings of teachers' lessons from her colleagues who paid for them, and is it permissible for the colleagues to give her the recordings without financial compensation from the student and without the teacher's permission?

If the lessons were recorded with the teacher's permission, there is no objection to benefiting from the recordings without the teacher's permission or a financial charge for students if they agree to lend them.

However, if they were recorded without the teacher's permission, the default is that it is impermissible. Nevertheless, some scholars permit it if it is for personal benefit and not for earning money. In this case, if you are in need of the lessons, there is no objection for you to act upon this opinion.